how to determine encoder resolution

Hello,
We wish to control an axis using servo motors. How do you determine how much resolution you need on the encoder. For example,
if we wanted a position accuracy of 0.1 arcseconds, how may counts per arcseconds is required by a servo system (standard PID servo controller)?
0.1 arcseconds = 10 counts / arcseconds. I sure you would like to over sample this with the encoder, but by how much: 2x, 5x, 10x, ??.
Is there a rule for servo system? I tried searching but couldn't find any references.
Thanks, Tony
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360 degrees x 3600 seconds per degree x 10 = 2.777778e-005 counts per revolution where the encoder is 1:1 direct for 360 degrees of rotation, but will need to be some multiple =>2 higher than that depending on the whole system and it's configuration to get an absolute resolution of 0.1 arcseconds. The higher the better and at 2.777778e-005 it would be absolute resolution of +/- 0.05 arcseconds per BIT in count, if I did this right. I would do 10x above to be safe. An absolute encoder is often not done 1:1 and this would change everything, need to look at whole position feedback system. There are far more elaborate systems for doing this as even the temperature could give you errors at this resolution.
try Google for "BEI encoders", "absolute encoders" and "absolute encoder telescope"
ALSO try NASA site.
http://dspace.dial.pipex.com/awr.tech/hhi.htm
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e+005, I'd wager
If the number is correct, and you use a 360 deg rotary encoder, you'd need 19-bit resolution, and a way for your control system to deal with 19-bit integers
Scott
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Tony Denault wrote:

How hard do you want your life to be, and how good is the plant at settling where you want it to?
10x will do the job if the job can be done at all, if your plant is really, _really_ well behaved less than 2x will do.
10x is implying a 360000 count encoder, which is pretty impressive. I'm not sure that you'll find anything with that resolution (note that you don't need 0.01 arc second _accuracy_ but you _do_ need 0.01 arc second _resolution_).
For that kind of accuracy and resolution you may need to use a high-speed resolver (which pretty much means using a multi-speed resolver). You may also want to consider a high-count optical encoder with interpolating outputs. There are a few out there that either interpolate internally and present you with the normal quadrature square outputs, and fewer yet that will present you with uninterpolated quadrature sine outputs which you then interpret like a resolver.
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controller)?
The old rule of thumb was half an order of magnitude. Of equal consideration is to make sure you have enough resolution for smooth velocity control if you are not using a tachometer on the system. Renishaw makes some very high resolution ring type incremental encoders and has the option for interpolation in the head for these. At Moore we manufacture a rotary work table with one of these encoders. We use an uninterpolated sinewave output with a line count of 16384 and then do our own interpolation in our controller at 4096x. By using 2 heads first order runout error is eliminated and we get some additional improvement by virtue of averaging the two heads. The final resolution on this type of axis is approximately 0.01 arc-seconds, and they have an uncompensated accuracy of less than 2 seconds. Jeff Lowe Moore Nanotechnology
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I'd consider an analog precision encoder with an output range cut down to your region of interest. Then your precision woes, at least for the encoder side, are taken care of by a simple 16-bit sampling.
Scott
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Scott: Do you mean something like : http://www.hohner.com/Data-Sheets/Absolute/Data-absolute-03-analog.htm ? If so, the precision is no where near the tenth of an arc-second regime. The OP was with the astronomy department, so a good assumption would be 360 degrees of rotation. Bottom line is that you need to resolve at least 12,960,000 counts per revolution minimum, and preferably an order of magnitude more. This is puts the required resolution somewhere between 24 and 27 bits of resolution if we are dealing with a sensor with only one or at most a few signal periods per revolution. At these levels I have found sine wave output incremental encoders to be better suited, and the demand for extreme precision analog systems is eliminated. The two names that come to mind for this type of work are Heidenhain and Renishaw.
Jeff Lowe Moore Nanotechnology
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That encoder no where near good enough. .05% of 360x3600x10 counts per revolution. Then you have to consider the error of the A/D input added to it.

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